用元学习加速量子热态制备，提升量子玻尔兹曼机训练效率。
Meta-learning of Gibbs states for many-body Hamiltonians with applications to Quantum Boltzmann Machines
- 提出元学习框架Meta-VQT与NN-Meta VQT，实现参数化哈密顿量的热态快速制备。
- 在2~8比特系统上验证，对未见参数仍具泛化能力，30倍提速现有方法。
- 适合量子机器学习、含噪中等规模量子设备上的热态生成任务。
量子吉布斯态的制备是量子计算中的基础挑战，对开放量子系统建模和量子机器学习至关重要。基于Cervera-Lierta等人（2021）提出的元变分量子本征值求解器框架及问题驱动的试探态设计，本文提出两种元学习算法：元变分量子热化器（Meta-VQT）与神经网络元变分量子热化器（NN-Meta VQT），用于在含噪中等规模量子（NISQ）设备上高效制备参数化哈密顿量的热态。Meta-VQT采用全量子试探态，而NN-Meta VQT结合量子-经典混合架构。两者均通过训练集上的集体优化，实现对未见参数的吉布斯态泛化制备。我们在最多8比特的横向场伊辛模型和2比特含所有场项的海森堡模型上验证了该方法，展示了超越训练数据的高效热态生成。对于更大系统，我们证明元学习得到的参数配合合理设计的试探态可作为优良初始值，在优化任务中显著优于随机初始化。此外，3比特基塔耶夫环例证了算法在有限温度相变区的有效性。最后，我们将算法应用于2比特海森堡模型的量子玻尔兹曼机（QBM）训练，实现了更高的训练效率、更优的吉布斯态精度，并相比基于变分量子虚时间（VarQITE）的QBM实现30倍的运行时加速，凸显了基于元算法的QBM在可扩展性与实用性上的优势。
原文摘要 · Abstract (English)
The preparation of quantum Gibbs states is a fundamental challenge in quantum computing, essential for applications ranging from modeling open quantum systems to quantum machine learning. Building on the Meta-Variational Quantum Eigensolver framework proposed by Cervera-Lierta et al.(2021) and a problem driven ansatz design, we introduce two meta-learning algorithms: Meta-Variational Quantum Thermalizer (Meta-VQT) and Neural Network Meta-VQT (NN-Meta VQT) for efficient thermal state preparation of parametrized Hamiltonians on Noisy Intermediate-Scale Quantum (NISQ) devices. Meta-VQT utilizes a fully quantum ansatz, while NN Meta-VQT integrates a quantum classical hybrid architecture. Both leverage collective optimization over training sets to generalize Gibbs state preparation to unseen parameters. We validate our methods on upto 8-qubit Transverse Field Ising Model and the 2-qubit Heisenberg model with all field terms, demonstrating efficient thermal state generation beyond training data. For larger systems, we show that our meta-learned parameters when combined with appropriately designed ansatz serve as warm start initializations, significantly outperforming random initializations in the optimization tasks. Furthermore, a 3- qubit Kitaev ring example showcases our algorithm's effectiveness across finite-temperature crossover regimes. Finally, we apply our algorithms to train a Quantum Boltzmann Machine (QBM) on a 2-qubit Heisenberg model with all field terms, achieving enhanced training efficiency, improved Gibbs state accuracy, and a 30-fold runtime speedup over existing techniques such as variational quantum imaginary time (VarQITE)-based QBM highlighting the scalability and practicality of meta-algorithm-based QBMs.
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